Getting past the guards
Related challenges: All Roads Lead to Dexter, Hazardous, Axed, Take em Down - Parts 1, 2 and 3
From the starting point, equip your Silverballers. Shoot the first guard you see - remember, it has to be a headshot. Quickly shoot two other guards to get "Take em Down - Part 1". You may need to restart the level, as you will most likely raise an alarm and Dexter will blow up the roof.
For "Take em Down - Part 2", push the first guard you see down the skylight. Sneak around and push the two other guards looking down into the skylight. Then sneak up the stairs and go right to the ledge. Garrote the closest guard and dump his body. There will be another guard sitting with his back to you. Wait till no other guards are nearby, then garrote and dump him as well. Then move forward unseen and kick the guard on your right off the ledge.
For "Take em Down - Part 3", push the first guard. Aim and shoot the second guard ahead who is looking through the skylight. Turn 90 degrees to your right and shoot the guard near the edge of the roof (not the one near the stairs). Then quickly go back and take cover behind the first dome before you are spotted. Guards who come to investigate dead bodies are easy targets to kill without being noticed. Clear out the segment of the roof before going up the stairs. If you didn't get the challenge yet, killing the three guards in this segment as in Part 2 will give you the challenge.
The easiest way is to push the first guard and get back to cover. On higher difficulties, another guard will come and stand opposite to the first guard's position. Push him off as well. Now take cover at the dome further away from the start point. While in cover, move right till you pass the guard in front of the stairs. Now get out of cover without being spotted and sneak past behind the guard, up the stairs. On the top of the stairs, if you wait for two guards to stop and talk below and shoot the concrete platform to kill them both, you get the "Hazardous" challenge. Now, kill the first guard as in "Take em Down - Part 2", but take his disguise before dumping his body. Move over to the left side of the roof. Wait till the guards are on the other side of the roof. Move ahead behind the benches. Then go right and instinct past the guards through the door. Pick up the keycard. Now go through the vent, up the stairs and scale the boxes and hang on the ledge. Shimmy past the first row of proximity mines and climb up. Then run forward and climb to the helipad, where Dexter is. This gets you the "All Roads Lead to Dexter" challenge.
Here the timer will stop, just as Dexter gets the news of Layla's death. Now go back the way you came, but instead of taking the vent, use instinct to avoid the landmines. Stick to your right and go past the guards unseen, behind the benches. Use the keycard to unlock the door. Inside you will get the evidence and a fire axe. Rush out with the fire axe and go on a killing spree. Get 5 kills before Dexter blows the roof to get the "Axed" challenge.
Dealing with Dexter
Related challenges: Stay on Target, It's Personal
Instead of going past the guards into the room with the keycard, you can instinct past the landmines safely when you are going towards Dexter for the first time. Then after you get on the helipad, sneak up behind Dexter and garrote him. You can pick up his weapon (Dexter's Ultramax) before the mission ends. This gets you both "Stay on Target" (if you are fast enough - in fact, you can skip killing the guards and use cover wisely to get to Dexter faster) and "It's Personal".
However, to get the evidence as well, climb up to the ledge to stop the timer and then go back. (If you want to get all items - specifically, the crowbar - then shoot the rod at the far end of the roof, ahead to the right of the helipad. It will blow up a few mines and clear a path to the crowbar. However, you may get spotted by Dexter while doing this.) After getting the evidence, instead of picking up the axe, check when the coast is clear and return, again through the landmines, to the helipad. Dexter will be more alert, so sneaking up on him might be more difficult, but it is doable. Fiber wire him to end the level. Note that you can get all of "Suit Only", "Infiltrator" and "Evidence Collector" using this method if you do not take a guard disguise.